Question

The standard IQ test has a mean of 97 and a standard deviation of 17. We want to be 95% certain that we are within 5 IQ points of the true mean. Determine the required sample size.

Answer 1

Solution :

Given that,

standard deviation = = 77

margin of error = E = 5

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= ((1.960 * 17) / 5)²

= 44.40

= 44

Sample size = 44